Gravitational wave detection by a spherical antenna: The angular sensitivity of resonators in the truncated icosahedral gravitational wave antenna configuration and its variation with sidereal time and galactic longitude

Experimental projects using spherical antennas to detect gravitational waves are nowadays a concrete reality. The main purpose of this paper is to give a possible way of interpreting output data from such a system. Responses of the five fundamental quadrupole modes and of the six resonators in truncated icosahedral gravitational wave antenna (TIGA) collocations are shown as a function of the incoming direction of the incident wave. Then, for a source lying in the galactic plane, sidereal time and galactic longitude dependence is given. Thus, once a candidate source of gravitational waves is considered, we can exactly predict the resonators’ response as a function of time.

Figure 1

Sensitivity of the five fundamental modes as a function of the GW arrival direction $(\theta ,\varphi ).$ The ratio ${ϵ}_{\alpha }$ is zero where the graph is darkest, and maximal ($\frac{3}{4}$) where the graph is lightest.

Figure 2

Sensitivity of the five fundamental modes as a function of the GW source position in the galactic plane, $(b),$ and of sidereal time in sidereal hours, ($t$), for a sphere near Leiden, NL (latitude $l=52.16°N$, longitude $L=4.45°E$). As in Fig. 1, the lightest zones indicate maximal values.

Figure 3

${ϵ}_0$ of Fig. 2 as a function of $t$ in sidereal hours for $b=0$ (source near the galactic center).

Figure 4

$|\tilde{q}(\omega ){|}^2$ with a sphere damping of ${10}^{-4}$, a resonator damping of ${10}^{-2}$, ${\omega }_0={10}^3\mathrm{Hz}$, $ϵ={10}^{-6}$, and ${\tilde{h}}^0(\omega )={10}^{-19}\mathrm{H}{\mathrm{z}}^{-1}$.

Figure 5

Sensitivity of the six resonators in TIGA configuration as a function of the GW arrival direction $(\theta ,\varphi )$. As in Fig. 1, the ratio $A_i$ is zero where the graph is darkest, and maximal where the graph is lightest.

Figure 6

The same as Fig. 5 for the sum of the $A_i$.

Figure 7

The same as Fig. 5, but as a function of sidereal hours (t) and galactic longitude (b) of the GW source, for a spherical detector near Leiden, NL, $l=52.16°N$, $L=4.45°E$.

Figure 8

Sum of the $A_i$ of Fig. 7 as a function of sidereal time for $b=0$, i.e. a source near the galactic center.